Geodesic
Theory of Dimension for Large Discrete Sets and Applications
A. Iosevich1 ; M. Rudnev2 ; I. Uriarte-Tuero3
1 Department of Mathematics, University of Rochester, Rochester, NY 14627
2 Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK
3 Department of Mathematics, Michigan State University, East Lansing MI 48824
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 5, pp. 148-169.

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We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections between the Erdős and Falconer distance problems in geometric combinatorics and geometric measure theory, respectively.
DOI : 10.1051/mmnp/20149510

A. Iosevich 1 ; M. Rudnev 2 ; I. Uriarte-Tuero 3

1 Department of Mathematics, University of Rochester, Rochester, NY 14627
2 Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK
3 Department of Mathematics, Michigan State University, East Lansing MI 48824 
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A. Iosevich; M. Rudnev; I. Uriarte-Tuero. Theory of Dimension for Large Discrete Sets and Applications. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 5, pp. 148-169. doi : 10.1051/mmnp/20149510. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149510/

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